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This article introduces a resampling procedure called the truncated geometric bootstrap method for stationary time series process. This procedure is based on resampling blocks of random length, where the length of each blocks has a truncated geometric distribution and capable of determining the probability p and number of block b. Special attention is given to problems with dependent data, and application with real data was carried out. Autoregressive model was fitted and the choice of order determined by Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). The normality test was carried out on the residual variance of the fitted model using Jargue-Bera statistics, and the best model was determined based on root mean square error of the forecasting values. The bootstrap method gives a better and a reliable model for predictive purposes. All the models for the different block sizes are good. They preserve and maintain stationary data structure of the process and are reliable for predictive purposes, confirming the efficiency of the proposed method.
This paper investigates the tolerable sample size needed for Ordinary
Least Square (OLS) Estimator to be used when there is presence of Multicollinearity
among the exogenous variables of a linear regression model. A regression model
with constant term (β0)
and two independent variables (with β1 and β2 as their respective
regression coefficients) that exhibit multicollinearity was considered. A Monte
Carlo study of 1000 trials was conducted at eight levels of multicollinearity
(0, 0.25, 0.5, 0.7, 0.75, 0.8, 0.9 and 0.99) and sample sizes (10, 20, 40, 80,
100, 150, 250 and 500). At each specification, the true regression coefficients
were set at unity while 1.5, 2.0 and 2.5 were taken as the hypothesized value.
The power value rate was obtained at every multicollinearity level for the
aforementioned sample sizes. Therefore, whether the hypothesized values highly
depart from the true values or not once the multicollinearity level is very
high (i.e. 0.99), the sample size
needed to work with in order to have an error free estimation or the inference
result must be greater than five hundred.
The purpose of this paper is to build a secured and reliable vehicle anti-theft system which will have the ability to access the vehicle subsystems from a remote location where there is GSM network. And also, the design method involves the interfacing of GSM/GPRS modem module with the vehicle ignition subsystem, and the test result shows that it performs some control actions on the vehicle subsystems from a mobile phone, having taken the advantage of the wide coverage area of some GSM networks. Hence the topic is “Remotely Controlled Vehicle Anti-theft System via GSM Network”.